MPLUS 1.04 prints out residual variances and R^2 for y* variables. Is it possible to constrain residual variances and therefore total variance of y* variables? e.g., residual variances may be hypothesized to be equal over time.

Long answer first. The residual variances are not parameters in the Mplus model, but we compute them as "remainders". So we don't have the possibility to constrain them to be equal over time. The Delta scale factors are parameters that are useful with categorical outcomes, but because they are inverted y* standard deviations they are functions of loadings, factor variances, as well as residual variances. So holding Delta's equal over time would only be the same as holding residual variances equal over time if the loadings and the factor variances were already held equal. Short answer: no.

This is a follow-up to the messages above: If you constrain the variance or residual variance of a variable to zero, do you also have to constrain all covariances with that variable to zero? And if so, why does the program still give you estimates if you don't constrain the covariances? Is it possible to test any hypothesized relationships with a variable for which you have constrained the variance or residual variance to zero?

In Version 2, if you fix a variance to zero, you also need to fix the covariances to zero. If you do not, you do get estimates. They are, however, not interpretable. In Version 3, if you use the | symbol and fix a variance to zero the covariances are automatically set to zero. This is not done using the BY option because the parameters are identified and someone may want to have access to them.

I AM USING EXAMPLE 8.7 AS TEH MODEL. EFA AND CFA OF THE FACTOR STRUCTURE WERE GOOD (FINALLY..) AFTER ACCOUNTING FOR DIRECT EFFECTS.

NOW I WANT TO MODEL THE HETEROGENIETY IN THE INITIAL STATUS AND RATE OF CHANGE. I AM GETTING THE CLASSIC ERRORS OF: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION.

i HAVE TRIED TO CONSTRAIN AND FREE UP PARAMETERS AD NAUSEUM BUT I AM MISSING SOMETHING. I ALSO CANNT TARGET HOW TO ADDRESS WHAT THE MESSAGE IS TELLING ME. I.E. CONDITION NUMBER IS 0.629D-18. PROBLEM INVOLVING PARAMETER 32.

WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN CLASS 1 IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/ RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE S1.

wHEN i ATTEMPT TO FREE PARAMETERS I LOSE THE STANDARD ERRORS PROBLEM BUT RETAIN THE WARNINGS IN ALL CLASSES. I ALSO TRIED TO MODIFY THE MODEL BY REDUCING THE CLASSES TO NO AVAIL.

I CAN SEE THAT THE SLOPES OF ONE OF MY VARIABLES ARE PRETTY FLAT FOR EACH CLASS (AS WELL AS THE OVERALL MEANS AS THEY CHANGE OVER THE 4 TIME PERIODS). THIS IS LIKELY THE SOURCE OF THE ISSUE BUT I THINK THERE IS ENOUGH VARIATION THERE BETWEEN CLASSES TO ULTIMATELY GET THIS MODEL TO CONVERGE.

I WAS ABLE TO GET 1/2 OF THE MODEL TO RUN (THE LEFT PART OF THE MODEL) BUT THE COMPLETE MODEL IS PROBLEMATIC.

Our LGM has five time-points. Since the observed outcome measures Y1>Y2>Y3>Y4>Y5, I expect the freely estimated time scores (i.e., the factor loadings associated with the latent slope growth factor) would have a pattern like (lambda5>lambda4> lambda3>lambda2>lambda1) with a negative slope growth factor. However, our model results show (lambda4=1.630>lambda5=1.390), indicating Y5>Y4 since the slope growth factor estimate was negative. Then, I respecify the time scores as: (lambda1=0 lambda2=1 lambda3=free lambda4=1.7, lambda5=1.8), and run the model again. I got very similar results for the two models, and both models fit data very well. Thus, I am wondering whether I could constrain (lambda5>lambda4> lambda3>lambda2>lambda1) in Mplus? Thanks a lot for your help!

The fact that the y scores (means of y) go down with time does not imply that the time scores decline - only that the slope mean is negative. You should let the time scores reflect the distance is timing of observations and only free them if a deviation from linearity is needed.

Glad to see your response to my question after coming back from a trip. Let me clarify my question: 1) the mean y scores declined over time (i.e., Y1>Y2>Y3>Y4>Y5) but did not change linearly. Thus, I freed some time scores. 2) y_hat =intercept+ slope*(time score). Suppose Intercept=10, Slope=-1.5, and time score=1.63 and 1.39 at time points t4 and t5, respectively. Then

y4_hat=10-1.5*1.63 y5_hat=10-1.5*1.39

Thus, y5_hat>y4_hat, i.e., mean y score increased, instead of declined, from t4 to t5. That was why I was wondering if I could put constraints on the time scores so that (y4_hat>y5_hat) can be ensured. Is it possible to put such constrains in Mplus?

I would not recommend trying to restrict the time scores but perhaps try to find another functional form for the growth curve such as a quadratic with a log time scale or a piecewise model if that seems to fit your data.

In a growth mixture model situation, how can the residual variances across the groups/classes be set to be unique to the different groups/classes? On pages 175 and 177 it is mentioned that residual variances across group are held constant. However, I cannot find anywhere in the manual where it discusses how to free the variances. Here is a bit of my code in a multiple group growth mixture model setting:

I had a non-significant negative variance for slope, so I set it to 0. Everything runs just fine, but I get only unstandardized output and I would like the beta weight (stdyx) for the path from condition (which is dichotomous) to slope. Is this impossible? Is there a formula I can use to generate it myself since the program doesn't?

I am modeling a multiple-group latent growth curve model of achievement test scores with 4 time points. I have 5 groups, each with more than 1,000 students.

When I ran the model, I got 4 negative residual variances (one for each group) that were non-significant, and I set those to zero. However, I have one significant (p<.05) residual variance for my last time point for the final group. In an earlier post, you recommended against setting this to zero and suggested modifying the model. Would you recommend this in my case? If so, what kinds of modifications would you suggest?

Hi, I am modeling a linear growth curve model and keep getting the not positive definitive matrix error regarding the growth factors. The output shows negative variances for the growth factors. In my notes from an Mplus seminar I noticed it says that outcome variables with decreasing variances over time are problematic. So I checked and mine are definitely decreasing over time.

I am trying to figure out whether there is a way to modify the model while retaining any existing variance in the growth factors (i.e., not setting them to zero). What options might I have?

As a follow up, I tried constraining the resid variances to be equal and that made the model worse. Then I tried fixing the covariance of the intercept and slope to zero (since it was not significant), but that didn't help. Only when I fix the slope variance to zero does the error go away.

So, does that mean it really should be fixed or that there is just a problem with the variances of the ouctome measures decreasing over time?

Yes. The mod indices pointed to the covariances between the growth factors and the middle two timepoints. Then I freed those timepoints and realized that there is really a non-linear pattern, with the vertex at the minimum point at my 2nd timepoint. However, can I model a quadratic slope with only 4 time points? Or should I model it as a piecewise model?

I may have a situation similar to Kathryn's above. I got 6 time points. The GMM (assuming variances of growth factors be the same across classes) works well. The residual variances for the 6 time points are between 18 to 33. Code:

However, when I consider having different variances of growth factors for 1 class (additional code:

%c#1% i s; s with i;

The residual variance for the last time point drops to nearly zero, making the plot of estimated means and observed individual values for that class very funny (variation for s1 to s5, but none at s6; all observed trajectories converge to the mean at s6). I have tried to (1) fix the residual variances to be the same across time, (2) delete the quadratic term, (3) reduce to two classes. The same problem persists.

It may happen because the variance of s is free in that class and may get large. You could instead let only the i variance be different. But as a first step you should do the analysis using the default class invariance of the variances, then use Mplus to plot the observed trajectories together with the estimated mean curve to visually inspect the need for having different variance in a class.

I did use the default class invariance of the variances, and the result is sensible. Based on the plot, I was trying to free the variances (i, s, s with i) for just 1 class. The problem then appears unless all slope variances are set to 0 (only i variances are different).

(1) I felt that the pattern (residual variance s6 drops to nearly 0 while all s1-s5 are fine) may imply some redundancy among the variances, which are now assumed different across class. But I don't understand why.

(2) Which model should be chosen? One model with all variances (i, s, s with i) but fixed to be equal across class. The other model has only i variances but allows to be different. The BIC points to the latter model though.

I'm running some GMM and, as I'm rather new with this analyses, I have two questions that may be pretty basic:

1) assuming variances (for intercepts and slopes) to be equal across classes my models convergence easily, and I obtain a meaningful two-class solution. Yet, when I allow variances to vary across classes I cannot make the model converge. Does it make sense to stuck to the first solution?

2)my variable is highly skewed, with a preponderance of zeros (at certain waves up to almost 90%). I'm using MLR but I'm wondering whether this is enough or whether the classes I found may be biased by the non-normality of my outcome (see Bauer & Curran, 2003).

1. I would use the PLOT command TYPE3 and look at the estimated means and observed individual curves to get an idea of where there is variability in the classes. I would then free the appropriate variances.

2. MLR is not sufficient when there are a preponderance of zeroes. If the variables are continuous, you can consider treating them as censored or using a two-part model.

I was trying to run growth curve null model with binary outcome for 7 time points. The result does not give me intercept .. while I ran null model with continous outcome with same data, it indeed give me both intercepts and slopes..

since when I ran the same model with stata, it gives me intercepts/slope, I am thining it is something to do with how M plus is working..?

Mplus uses a different parametrization for categorical growth models. The thresholds are held equal across time, the intercept growth factor mean is fixed at zero, and the slope growth factor mean is free.

With continuous outcomes, intercepts are fixed at zero and the intercept and growth factor means are free.

could I ask a follow- up question? strangely, the intercept I got from LGM approach (M plus) and from multi level approach(stata) is very different. when I tested with a continous outcome, the number is almost same or very similar which is expected in a null model--

the multi level intercept is a coefficient I got from multinomial mixed effect regression. should I do something to M plus to get the same result?

Dear all, Reading from the top concerning the rekommendations (not) to constrain the residuals to equality I wonder whether this still stands if such constraints render a model, that otherwise would be just identified, over identified .

This concerts simpel three timepoints linear growth with a slope mean close to zero.

the unconstrianed model has a df of 1 (but a Chi2<df, cfi =1 and rmsea=0). I do not have negative residual variances but very close variance etsimates of T1 and T2 on residuals (2.896 ad 2.427) and slightly decreasing res-variances from T1 to T3. The slope mean is very close to zero, -0.007 (0.047).

I cannot seem to find the source of misssepcification. This growth curve is meant to be included in a paralell LGC, the second curve is specified similarily and returns interpretable fit indices, so there ought to be some parameter estimates which are causing this issue with identifcation, would you agree? Do you have a suggestion for how to spot the potential missspecification?

I have a sample of >700. Doesn't the fit indicate a just identified model?

WHen freeing the residuals, the slope variance was non-signficant. I have now constrained slope variance to zero, and have gotten a significant chi2 but other fit indices are well acceptable now. WHat is your take on this approach?

Hi, i am running GMM, and the mean growth factors and class membership change quite dramatically by freeing the residual var across classes. Both models converge fine without any issues. In this case, which model would you recommend that I choose (default vs. free res var across classes)? [I also set the var and cov of growth factors to vary across classes. All other parameters follow the default.] Does algorithm Mplus use have any assumptions about the mixture distributions in terms of equal residual variances across classes? Thank you in advance.

I recommend first running with the Mplus default of equal variances (residual and growth factor) and then check the individual observed curves sorted into most likely class (we have that plot option). There you can see if there is one class that has much more/less spread than others around the class mean curve - and free variances there. Sometimes the residual variances is what should be freed and sometimes you get more benefit from freeing say only the intercept growth factor variance.

Hi, I am running an unconditional latent growth model and the model seems to run well. No errors on output. However, for my intercept value (which was 0.00), the p-value and est/s.e. was 999. Also, the intercept and the s.e. of the intercept cannot be 0.00. It should be higher than that. Can you explain to me why the intercept looks weird. The slope was estimated just fine.